Nonlinear Conservation Laws Fluid Systems and Related Topics 1st Edition by Gui Qiang Chen, Ta Tsien Li, Chun Liu ISBN 9814273279 978-9814273275

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Product details:

ISBN 10: 9814273279

ISBN 13: 978-9814273275 

Author: Gui-Qiang Chen, Ta-Tsien Li, Chun Liu 

This book is a collection of lecture notes on Nonlinear Conservation Laws, Fluid Systems and Related Topics delivered at 2007 Shanghai Mathematics Summer School held at Fudan University, China, by world’s leading experts in the field.The volume comprises ?ve chapters that cover a range of topics from mathematical theory and numerical approximation of both incompressible and compressible ?uid ?ows, kinetic theory and conservation laws, to statistical theories for ?uid systems. Researchers and graduate students who want to work in this field will benefit from this essential reference as each chapter leads readers from the basics to the frontiers of the current research in these areas.

Table of contents:

Book 1 (Euler Equations & Vorticity)

1. Introduction

2. Derivation and exact solutions

3. Local well-posedness of the 3D Euler equation

4. The BKM blow-up criterion

5. Recent global existence results

6. Lower dimensional models for the 3D Euler equations

7. Vortex patch
   References

Book 2 – Denis Serre

Systems of Conservation Laws. Theory, Numerical Approximation and Discrete Shock Profiles

1. Hyperbolic systems of conservation laws

2. Finite difference schemes

3. Discrete shock profiles

Book 3 – Seiji Ukai, Tong Yang

Kinetic Theory and Conservation Laws: An Introduction

1. Introduction

2. Expansions and their unification

3. Detour to hyperbolic conservation laws

4. Spectral analysis on the linearized Boltzmann operator

5. Global existence and convergence rates

Book 4 – Xiaoming Wang

Elementary Statistical Theories with Applications to Fluid Systems

1. Introduction

2. Stationary statistics

3. Remarks on time dependent statistics
   Appendix: some useful theorems
   References

Book 5 – Yuxi Zheng

The Compressible Euler System in Two Space Dimensions

1. Physical phenomena and mathematical problems

2. Characteristic decomposition of the pseudo-steady case

3. The hodograph transformation and the interaction of rarefaction waves

4. Local solutions for quasilinear systems

5. Invariant regions for systems

6. The pressure gradient system

7. Open problems

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Tags: Gui Qiang Chen, Ta Tsien Li, Chun Liu, Nonlinear, Conservation Laws, Fluid Systems, Related Topics